Algebraic Cycles on Real Varieties and Z/2-Equivariant Homotopy Theory

Abstract

In this paper the spaces of algebraic cycles on a real projective variety X are studied as Z/2-spaces under the action of the Galois group Gal (C/R). In particular, the equivariant homotopy type of the group of algebraic p-cycles $\mathcal{Z}_p(\mathbb{P}_{\mathbb{C}}^n)$ is computed. A version of Lawson homology for real varieties is proposed. The real Lawson homology groups are computed for a class of real varieties. 2000 Mathematical Subject Classification: primary 55P91; secondary 14C05, 19L47, 55N91.

Author notes

This research was supported in part by FCT (Portugal) under the programme POCTI.

Current address: Departamento de Matemática, Instituto Superior Técnico, Avenida Rovisco Pais, 1049-001 Lisbon, Portugal.